NIMCET 2020
Vertices of the vectors , and form a triangle. This triangle is
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B — Right angle triangle
Detailed Solution
The vertices are P(1, −2, 2), Q(2, 1, −1) and R(3, −1, 2). Then , and .
, so the angle at R is 90°.
✓ Check
.⚠ Common trap
(C) fails: the side lengths , and are all different.Quick tip
: Pythagoras holds, so it is right-angled
💬 Discussions on this question
Ask a doubt ›Still stuck on this question? Ask our faculty and fellow students — answers appear here.
Ask a doubtMore Vectors Questions
View all ›- Q1.If , and , then depends on
- Q2.If and are unit vectors such that , then which of the following statements is true?
- Q3.A vector of magnitude 5 units makes equal angles with each of the three mutually perpendicular coordinate axes. The sum of the magnitudes of its projections on the three axes is
- Q4.If and , then the value of is
- Q5.Let and . If is a vector such that , the angle between and is , and , then the value of is
More Quantitative Aptitude Questions
- Q1.By selling 45 lemons for ₹40, a man loses 20%. How many lemons should he sell for ₹24 to gain 20%?Profit, Loss & Discount
- Q2.The marked price of an article is 1.45 times its cost price. Its selling price is ₹1,500 and the profit is 25%. What is the discount percentage? Profit, Loss & Discount
- Q3.Let A be a real number. Then the roots of the equation are real and distinct if and only if Quadratic Equations
- Q4.The number of distinct real roots of the equation is Quadratic Equations
- Q5.The roots of are:Quadratic Equations
Vectors — Preparation
This question tests your understanding of Vectors, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
A vector is a quantity with both magnitude and direction, such as displacement or force. This topic covers types of vectors (zero, unit, collinear, coplanar and position vectors), vector addition, multiplication by a scalar, the section formula, and the components of a vector along the i, j and k axes. It also covers the scalar (dot) product and its use in finding the angle between two vectors and the projection of one vector on another, the vector (cross) product and its use in finding areas of parallelograms and triangles, and the scalar triple product for the volume of a parallelepiped and the condition for coplanarity. Remember that two vectors are perpendicular when their dot product is zero, parallel when their cross product is the zero vector, and three vectors are coplanar when their scalar triple product is zero. Practise the vectors questions below, each with a step-by-step solution.